- #1
calcuseless
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Homework Statement
Inside the sphere x2 + y2 + z2 = R2 and between the planes z = [tex]\frac{R}{2}[/tex] and z = R. Show in cylindrical and spherical coordinates.
Homework Equations
[tex]\iiint\limits_Gr\,dz\,dr\,d\theta[/tex]
[tex]\iiint\limits_G\rho^{2}sin\,\theta\,d\rho\,d\phi\,d\theta[/tex]
The Attempt at a Solution
[tex]2\int_0^{2\pi}\int_0^{R\sqrt{\frac{3}{4}}}\int_?^{\sqrt{R^{2}-r^{2}}}r\,dz\,dr\,d\theta[/tex]
Is my upper limit for r correct? How do I find the lower limit for z?
[tex]\int_0^{2\pi}\int_0^{\frac{\pi}{3}}\int_?^R\rho^{2}sin\,\theta\,d\rho\,d\phi\,d\theta[/tex]
How do I find the lower limit for rho?